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The first order sensitivity analysis is performed for a class of optimal control problems for time delay parabolic equations in which retarded arguments appear in the integral form with h ∊ (0,6). The optimality system is analyzed with the respect to a small parameter. The directional derivative of the optimal control is obtained as a solution to an auxiliary optimization problem. The control constraints...
The standard topological derivative methodology developed by the authors in many papers requires knowledge of point-wise values of solutions to partial differential equations or variational equalities. However, the contact or unilateral problems are studied in the energy space setting, wsznumer2005here point-wise values are not defined. The authors proposed the approach based on domain decomposition...
In the paper the first order sensitivity analysis is performed for a class of optimal control problems for parabolic-hyperbolic systems in which time delays appear both in the state equations and in the Neumann boundary conditions. A singular perturbation of geometrical domain of integration is introduced in the form of a circular hole. The Steklov-Poincaré operator on a circle is defined in order...
We introduce the Griffith shape functional as the distributed shape derivative of the elastic energy evaluated in a domain with a crack, with respect to the crack length. We are interested in the dependence of this functional on domain perturbations far from the crack. As a result, the directional shape and topological derivatives of the nonsmooth Griffith shape functional are obtained with respect...
The aim of this paper is to perform sensitivity analysis of optimal control problems defined for the wave equation. The small parameter describes the size of an imperfection in the form of a small hole or cavity in the geometrical domain of integration. The initial state equation in the singularly perturbed domain is replaced by the equation in a smooth domain. The imperfection is replaced by its...
The non stationary, compressible Navier-Stokes equations are considered in a bounded hold-all domain. The nonhomegeneous boundary conditions are prescribed on the boundary of hold-all domain. The existence of the so-called weak normalized solutions for the model is established in [2]. In this talk we consider the associated shape optimization problems for the model. In the stationary case the drag...
In the paper the first order sensitivity analysis is performed for a class of optimal control problems for parabolic-hyperbolic equations. A singular perturbation of geometrical domain of integration is introduced in the form of a circular hole. The Steklov-Poincaré operator on a circle is defined in order to reduce the problem to regular perturbations in the truncated domain. The optimality system...
We consider an elastic body with a rigid inclusion and a crack located at the boundary of the inclusion. It is assumed that non-penetration conditions are imposed at the crack faces which do not allow the opposite crack faces to penetrate each other. The differentiability of the elastic energy with respect to the crack length, for the crack located at the boundary of rigid inclusion, is established.
In the paper the first order sensitivity analysis is performed for a class of optimal control problems for infinite order hyperbolic equations. A singular perturbation of geometrical domain of integration is introduced in the form of a circular hole. The Steklov-Poincaré operator on a circle is defined in order to reduce the problem to regular perturbations in the truncated domain. The optimality...
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